Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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RINGS IN WHICH EVERY IDEAL CONTAINED IN THE SET OF ZERO-DIVISORS IS A D-IDEAL

  • Anebri, Adam (Laboratory of Modelling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez University S.M. Ben Abdellah Fez) ;
  • Mahdou, Najib (Laboratory of Modelling and Mathematical Structures Department of Mathematics Faculty of Science and Technology of Fez University S.M. Ben Abdellah Fez) ;
  • Mimouni, Abdeslam (Department of Mathematics and Statistics King Fahd University of Petroleum & Minerals)
  • Received : 2020.12.16
  • Accepted : 2021.04.15
  • Published : 2022.01.31
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Abstract

In this paper, we introduce and study the class of rings in which every ideal consisting entirely of zero divisors is a d-ideal, considered as a generalization of strongly duo rings. Some results including the characterization of AA-rings are given in the first section. Further, we examine the stability of these rings in localization and study the possible transfer to direct product and trivial ring extension. In addition, we define the class of dE-ideals which allows us to characterize von Neumann regular rings.

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References

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